Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22588470 | C2 | semidirect |
| 3. #22587086 | C2 | semidirect |
| 6. #22586200 | C2 | semidirect |
| 7. C71×#1286 | C2 | semidirect |
| 11. #17986076 | C4 | semidirect |
| 13. #17986064 | C4 | semidirect |
| 175. #1286 | D71 | semidirect |
| 176. C71 | #8680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597051 | 2 |
| #22588470 | 2 |
| #22587086 | 2 |
| #22586901 | 2 |
| #22586899 | 2 |
| #22586200 | 2 |
| C71×#1286 | 2 |
| #8680 | 71 |